The index of a metric plays significant roles in differential geometry as it generates variety of vector fields such as space-like, time-like, and light-like fileds. With the help of these vector fields, we establish interesting properties on ( )-Sasakian manifolds, which was introduced by Bejancu and Duggal [1] and further investigated by Xufeng and Xiaoli [2]. Since Sasakian manifolds with in...

We derive new, sharp lower bounds for certain curvature functionals on the space of Riemannian metrics of a smooth compact 4manifold with a non-trivial Seiberg-Witten invariant. These allow one, for example, to exactly compute the infimum of the L2-norm of Ricci curvature for all complex surfaces of general type. We are also able to show that the standard metric on any complex hyperbolic 4manif...

A Buekenhout-Tits unital is defined to be a unital in PG(2, q2) obtained by coning the Tits ovoid using Buekenhout’s parabolic method. The full linear collineation group stabilizing this unital is computed, and related design questions are also addressed. While the answers to the design questions are very similar to those obtained for Buekenhout-Metz unitals, the group theoretic results are qui...

We show that a suitable 2-dimensional linear system of Hermitian curves of PG(2, q2) defines a model for the Desarguesian plane PG(2, q). Using this model we give the following group-theoretic characterization of the classical unitals. A unital in PG(2, q2) is classical if and only if it is fixed by a linear collineation group of order 6(q + 1)2 that fixes no point or line in PG(2, q2).

Some associativity properties of a loop can be interpreted as certain closure configuration of the corresponding 3-net. It was known that the smallest non-associative loops with the so called left Bol property have order 8. In this paper, we determine the direction preserving collineation groups of the 3-nets belonging to these smallest Bol loops. For that, we prove some new results concerning ...

If F is an involution and φ a suitable collineation, then φ ◦ F ◦ φ−1 is an involution; this form includes well-known conjugacies and new conjugacies, including aleph, beth, complementary, and anticomplementary. If Z(U) is the self-isogonal cubic with pivot U , then φ carries Z(U) to a pivotal cubic. Particular attention is given to the Darboux and Lucas cubics, D and L, and conjugacy-preservin...

Abstract. We present a General Linear Camera (GLC) model that unifies many previous camera models into a single representation. The GLC model is capable of describing all perspective (pinhole), orthographic, and many multiperspective (including pushbroom and two-slit) cameras, as well as epipolar plane images. It also includes three new and previously unexplored multiperspective linear cameras....

In this paper, we study projection systems with a single effective viewpoint, including combinations of mirrors and lenses (catadioptric) as well as just lenses with or without radial distortion (dioptric systems). First, we extend a well-known unifying model for central catadioptric systems to incorporate a class of dioptric systems with radial distortion. Second, we provide a new representati...